Large mode area optical fibers with bend compensation

ABSTRACT

A LMA, single-mode optical fiber comprises a core region, an inner cladding region surrounding the core region, and an outer cladding region surrounding the inner cladding region. The inner cladding region is configured to provide bend compensation. In one embodiment the index profile of the inner cladding region is graded with a slope of γn core /R b , where n core  is the refractive index of the core region, R b  is the bend radius, and γ=0.6-1.2. In addition, the inner cladding is annular and the ratio of its outer radius to its inner radius is greater than 2. In a preferred embodiment this ratio is greater than 3. The overall index profile may be symmetric or asymmetric.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from two provisional applications: Ser.No. 61/506,631 filed on Jul. 11, 2011 and Ser. No. 61/419,420 filed onDec. 3, 2010.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to large-mode-area (LMA) fibers designed tocompensate for the effects of bends in the fiber and to suppresshigher-order modes (HOMs) and, more particularly to high power opticalamplifiers that incorporate such LMA fibers.

2. Discussion of the Related Art

Optical fiber amplifiers have great impact in diverse applicationsranging from high power devices used for cutting, welding and rangefinding to lower power devices used to amplify optical carrier signalsin telecommunication systems. In the former case, the high poweramplifier utilizes a gain-producing fiber (GPF; e.g., a LMA fiber dopedwith suitable rare-earth species or chromium) and a source of pump lightto amplify signal light propagating in effectively a single mode (i.e.,the fundamental transverse mode) through the LMA fiber.

LMA fibers, which have a relatively large effective area (A_(eff)), areused to reduce optical power density and, therefore, also reduce opticalnonlinearities in the fiber. However, larger area fibers typicallysupport several or many modes, increasing the likelihood that HOMs willalso propagate in the fiber and undergo amplification, thereby degradingthe quality of beam. Beam quality is often characterized in terms of aparameter known as M² (M²=1 for an ideal Gaussian beam), whereas singlemodedness can be characterized by various techniques including spatiallyand spectrally (S²) resolved imaging, as described by Nicholson et al.,Optics Express, Vo. 16, No. 10, pp. 7233-7243 (2008), which isincorporated herein by reference. Bends in the fiber exacerbate thisproblem—they reduce the ability of various fiber designs to selectivelysuppress HOMs while ensuring propagation of the fundamental mode atpower levels that satisfy typical performance requirements.

In a typical conventional amplifier configuration a few meters (e.g., 5m) of GPF is coiled within an amplifier package that may also containother components of the amplifier. In some designs, those componentsinclude a non-GPF LMA (e.g., a fiber pigtail) optically coupled to theGPF. Coiling the LMA fiber, an expedient to save space, means that thefiber is bent.

Bends in the LMA fiber are a key factor imposing performance tradeoffsbetween three principal goals of LMA fiber design: large mode area, lowloss, and single-mode operation. Macrobend loss is often the dominantsource of loss, bend distortion limits the scaling of area, and bendsdegrade single-mode operation, as noted above, by limiting the degree towhich unwanted HOMs can be selectively suppressed.

One strategy for ameliorating the adverse effects of bending is topre-compensate the refractive index profile of an unbent (as-fabricated,straight) fiber for the expected bend-induced perturbation, as describedby Fini, Opt. Express, Vol. 14, No. 1, pp. 69-81 (2006), which isincorporated herein by reference. This strategy, which utilizes anasymmetric index profile, has been exploited by others in the design ofbend-compensated microstructure fibers. [See, for example, Minelly, U.S.Pat. No. 7,876,495 (2011), which is also incorporated herein byreference.] However, this strategy may be difficult to implement. Itrequires an asymmetric index profile across the fiber cross-section, andit requires deployment of the fiber in a fixed azimuthal orientationthroughout the bend.

By the terms unbent, straight, and as fabricated we mean the bend radiusof the fiber is essentially infinite (a perfectly straight fiber) or solarge that any resulting bend would have an insignificant effect on thefiber performance for the intended application of the fiber.

Thus, there is a need for an LMA fiber design that provides bendcompensation without requiring an asymmetric index profile. That is,there is a need for a fiber design that provides bend compensation inLMA fibers that have either asymmetric or symmetric index profiles.

In addition, there is a need for a LMA fiber design that provides forHOM suppression in addition to compensation.

BRIEF SUMMARY OF THE INVENTION

Our analysis of bends in LMA fibers has uncovered a surprisingresult—the selectivity of HOM suppression is degraded primarily by thebend perturbation of the inner cladding region, not by perturbation ofthe core region or other regions of the fiber. Thus, to dramaticallyimprove the basic performance tradeoff it is sufficient to compensatethe bend perturbation in the inner cladding region. Unlike the priorart, bend compensation accompanied by sufficient HOM suppressionrequires neither asymmetry of the index profile of the core region norasymmetry of the index profile across the entire fiber cross-section.However, the principal design features of our invention do not excludethe use of asymmetric index profiles either.

In accordance with a first aspect of our invention, a bend-compensatedoptical fiber comprises a core region having a longitudinal axis and acladding region surrounding the core region. The core and claddingregions are configured to support and guide the propagation of signallight in a fundamental transverse mode in the core region in thedirection of the fiber axis. The cladding region includes an innercladding region surrounding the core region and an outer cladding regionsurrounding the inner cladding region. At least a longitudinal segmentof the fiber is configured to be bent or coiled to a bend radius R_(b).(Bending changes a gradient of the index profile of a straight fiber,producing what is known in the art as an equivalent index profile withinthe bent segment.) At least the longitudinal fiber segment ispre-compensated in that (i) the transverse cross section of the fiberhas a refractive index profile that is approximately azimuthallysymmetric with respect to the fiber axis and (ii) the refractive indexof at least a transverse portion of the inner cladding region is gradedwith a slope configured to compensate for the expected change of theindex profile that would be induced by the bend; that is, to compensatefor the expected equivalent index profile.

In one embodiment of the first aspect of our invention, bendcompensation of our LMA fiber, with excellent HOM suppression to enableeffectively single-mode operation, is achieved by grading the refractiveindex of the inner cladding region of the LMA fiber, preferably with aslope γn_(core)/R_(b), where γ falls in the range 0.6-1.2; where γ=1corresponds to ideal compensation assuming the well-known geometricalconformal mapping [see, Marcuse, Appl. Opt., Vol. 21, p. 4208 (1982),which is incorporated herein by reference.], but preferred designs mayinclude a stress correction (e.g., γ=0.8) or other adjustments thatallow for curvature variations within a coil, etc; n_(core) is the indexof the core region; and R_(b) is the bend radius. [Regarding,bend-induced strain (stress), see, Nagano, Applied Optics Vol. 17, No.13, pp. 2080-2085 (1978), which is also incorporated herein byreference.]

In another embodiment of the first aspect of our invention, the innercladding region is annular having an inner radius r₁ and an outer radiusr₂ such that the ratio r₂/r_(core) is configured to suppress thepropagation of HOMs. In some embodiments we prefer r₂/r_(core)>2 and inothers we prefer r₂/r_(core)>3 depending on the desired level of HOMsuppression.

In accordance with a second aspect of our invention, a bend-compensatedoptical fiber comprises a core region having a longitudinal axis and acladding region surrounding the core region. The core and claddingregions are configured to support and guide the propagation of signallight in a fundamental transverse mode in the core region in thedirection of the fiber axis. The cladding region includes an innercladding region surrounding the core region and an outer cladding regionsurrounding the inner cladding region. At least a longitudinal segmentof the fiber is configured to be bent or coiled to a bend radius R_(b)and at least the longitudinal segment is pre-compensated in that therefractive index of at least a transverse portion of the inner claddingregion is graded with a slope configured to compensate for the expectedchange in the index profile that would be induced by the bend; that is,to compensate for the equivalent index profile. In addition, the innercladding region is annular having an inner radius r₁ and an outer radiusr₂ such that the ratio r₂/r_(core) is configured to suppress thepropagation of HOMs. In some embodiments of the second aspect of ourinvention, we prefer r₂/r_(core)>2 and in others we prefer r₂/r_(core)>3depending on the desired level of HOM suppression.

In some embodiments of the second aspect of our invention, at least alongitudinal segment of the fiber is configured to be bent or coiled toa bend radius R_(b) and within the segment the transverse cross sectionof the fiber has a refractive index profile that is approximatelyazimuthally symmetric with respect to the fiber axis. These symmetricembodiments enable the fiber to be deployed without requiring a fixedazimuthal orientation.

In other embodiments of the second aspect of our invention, at least alongitudinal segment of the fiber is configured to be bent or coiled toa bend radius R_(b) and within the segment the transverse cross sectionof the fiber has a refractive index profile that is asymmetric withrespect to the fiber axis.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

Our invention, together with its various features and advantages, can bereadily understood from the following more detailed description taken inconjunction with the accompanying drawing, in which:

FIG. 1A is a schematic, transverse cross-section of a bend-compensatedLMA optical fiber in accordance with one embodiment of our invention;

FIG. 1B is a schematic graph of an illustrative symmetric refractiveindex profile of the fiber of FIG. 1A;

FIG. 2 shows schematic graphs of the refractive index profiles of aconventional step-index-core (SIC) fiber, wherein the fiber has beensubjected to a relatively loose bend (FIG. 2A) and a relatively tighterbend (FIG. 2B);

FIG. 3 shows schematic graphs of the refractive index profiles of abend-compensated SIC fiber in accordance with an illustrative embodimentof our invention, wherein the fiber has been subjected to no bend (FIG.3A) and a relatively tight bend (FIG. 3B);

FIG. 4 shows schematic graphs of the relative refractive index profilesof a symmetric bend-compensated (SBC) fiber in accordance with anotherillustrative embodiment of our invention, wherein the fiber has beensubjected to no bend (FIG. 4A) and a bend having a radius R_(b)=15 cm(FIG. 4B);

FIG. 5 shows schematic graphs of the refractive index profiles of a SBCfiber in accordance with yet another illustrative embodiment of ourinvention, wherein the fiber has been subjected to no bend (FIG. 5A) anda bend having a radius R_(b)=15 cm (FIG. 5B);

FIG. 6 shows a series of graphs of HOM loss vs. effective area (A_(eff))comparing simulated results for a conventional SIC fiber (curve 6.6), aparabolic core index fiber (curve 6.5) and a multiplicity of SBC opticalfibers in accordance with various embodiments of our invention (curves6-1-6.4);

FIG. 7 shows schematic graphs of the relative refractive index profilesof an asymmetric bend-compensated (ABC) fiber in accordance with anotherillustrative embodiment of our invention, wherein the fiber has beensubjected to no bend (FIG. 7A) and a bend having a radius R_(b)=15 cm(FIG. 7B). In addition, FIG. 7C is a grayscale depiction of the indexprofile shown in FIG. 7A. Higher index is shown in light gray and white,whereas lower index is shown as dark gray and black;

FIG. 8 shows a series of graphs of HOM loss vs. effective area (A_(eff))comparing simulated results for a conventional SIC fiber (curve 8.6), aparabolic core index fiber (curve 8.5) and six ABC optical fibers inaccordance with various embodiments of our invention (three data points8.2 and three data points 8.3);

FIG. 9 is a schematic block diagram depicting an illustrative opticalfiber amplifier employing a LMA GPF in accordance with an illustrativeembodiment of our invention;

FIG. 10 is a schematic, isometric view of a subassembly in which acoiled fiber is mounted within a groove on a plate in accordance with anillustrative embodiment of our invention; and

FIG. 11 is a schematic, isometric view of another subassembly in which acoiled fiber is mounted on a mandrel in accordance with anotherillustrative embodiment of our invention.

Various ones of the foregoing figures are shown schematically in thatthey are not drawn to scale and/or, in the interests of simplicity andclarity of illustration, do not include all of the details of an actualoptical fiber or product depicted. In addition, note that the ordinateof FIG. 1B shows the absolute refractive index, whereas the ordinates ofFIGS. 4, 5 and 7 show the relative refractive index (i.e., indices arerelative to the refractive index of the outer cladding region).

GLOSSARY

Bending: Macro-bending, commonly referred to as simply bending, takesplace when a fiber is bent, coiled or curled so that its curvature isrelatively constant along its length. In contrast, micro-bending takesplace when curvature changes significantly within the adiabatic lengthscale for a particular fiber (e.g., along fiber lengths on the order ofa millimeter or less). Such micro-bends are formed, for example, instandard micro-bending tests by pressing the fiber into sand paper.

Center Wavelength: Throughout this discussion references made towavelength are intended to mean the center wavelength of a particularlight emission, it being understood that all such emissions have acharacteristic linewidth that includes a well-known range of wavelengthsabove and below the center wavelength.

Glass Fiber: Optical fiber of the type described herein is typicallymade of glass (e.g., silica) in which the refractive indices of the coreregion and of the cladding region are controlled by the amount and typeof one or more dopants (e.g., P, Al, Ge, F, Cl) or by hollow voidsincorporated therein during the fabrication of the fiber, as is wellknown in the art. These refractive indices, as well as thethicknesses/diameters of core/cladding regions, determine importantoperating parameters, as is well known in the art. In order for suchglass fibers to produce gain when suitably pumped, they are also dopedwith a rare-earth species or chromium, as mentioned previously.

Index: The terms index and indices shall mean refractive index andrefractive indices. In designs where a particular region (e.g., acladding region) includes microstructure [e.g., holes, whether filled(e.g., with a low-index gas, liquid or solid) or unfilled (e.g.,air-holes)], then the index of such a region is interpreted to mean theaverage index seen by light propagating in that region.

Index Profile: The schematic index profiles of FIGS. 1B, 2-5 and 7 areaverages of the actual minute variations of index that would beobservable in an optical fiber. In addition, although various regions ofthe index profile are shown as being rectangular, the boundaries of suchregions need not be horizontal or vertical; one or more may be slanted,for example, the region may be trapezoidal or triangular.

LMA: In high-power applications, a large mode area (LMA) fiber isdefined as having a fundamental mode effective area greater than orapproximately equal to 90λ², where λ is the signal wavelength. Forexample, at a wavelength of 1060 nm (1.06 μm), an effective area around100 μm² or greater constitutes a large mode area, whereas at awavelength of at 1550 nm (1.55 μm) an effective area of 216 μm² orgreater constitutes large mode area. Bend compensation becomesparticularly important for larger mode areas of around 300λ² or greater.

M²: The optical characteristics of a LMA fiber sensitively depend uponthe details of its transverse refractive index profile. Conventionalwisdom dictates that desirable LMA fibers have a fundamental mode withM² very near to 1.0, meaning that the optical field of the fundamentaltransverse mode is very nearly Gaussian in shape under the assumptionthat the transverse refractive index profile inside the core region isessentially uniform; that is, the refractive index profile isessentially uniform within the transverse cross-section of the coreregion. M² measures the similarity between the mode field and a trueGaussian function. More specifically, M²=1.0 for a mode having aGaussian shape, and M²>1.0 for all other mode field shapes.

M² defines the similarity that the fundamental transverse mode of thefiber has to an ideal Gaussian function, as described by P. A. Belanger,Optical Engineering, Vol. 32. No. 9, pp. 2107-2109 (1993), which isincorporated herein by reference. (Although this paper defines M² forLP₀₁ fundamental mode of a step-index optical fiber, the definition isvalid for all optical fibers described herein.) In theory M² may bearbitrarily large, but in practice M² for GPFs is typically in therange, 1<M²<10, approximately. Moreover, M²˜1.06 is typically consideredto be small in the sense of M²˜1.0, for example, whereas M²˜1.3 isconsidered to be large in the sense of M²>>1.0, for example.

When M² is very near to 1.0 the beam emerging from the fiber may beefficiently collimated or tightly focused to a diffraction limited spot.

Mode: The term mode(s) shall mean the transverse mode(s) of anelectromagnetic wave (e.g., signal light, which includes signal light tobe amplified in the case of an optical amplifier or the stimulatedemission in the case of a laser).

Mode size: The size of an optical mode is characterized by its effectivearea A_(eff), which is given by:

$A_{eff} = \frac{\left( {\int{{E}^{2}{\mathbb{d}A}}} \right)^{2}}{\int{{E}^{4}{\mathbb{d}A}}}$where E is the transverse spatial envelope of the mode's electric field,and the integrations are understood to be performed over thecross-sectional area of the fiber. When the mode-field shape is close toan axisymmetric (i.e., symmetric about the longitudinal axis of rotationof the fiber) Gaussian function, the mode-field diameter (MFD) is anappropriate metric for the diameter of the mode and may be expressed as:

${M\; F\; D} = {2\sqrt{\frac{2{\int{{E}^{2}{\mathbb{d}A}}}}{\int{{\frac{\mathbb{d}E}{\mathbb{d}r}}^{2}{\mathbb{d}A}}}}}$where r is the radial coordinate. When the mode-field shape is exactlyequal to an axisymmetric Gaussian function, then A_(eff)=π×MFD²/4.

Radius/Diameter: Although the use of the terms radius and diameter inthe foregoing (and following) discussion implies that the cross-sectionsof the various regions (e.g., core, pedestal, trench, cladding) arecircular and/or annular, in practice these regions may be non-circular;for example, they may be elliptical, polygonal, irregular or other morecomplex shapes. Nevertheless, as is common in the art, we frequently usethe terms radius and/or diameter for simplicity and clarity.

Signal Propagation: Although signal light may actually crisscross thelongitudinal axis as it propagates along a fiber, it is well understoodin the art that the general direction of propagation is fairly stated asbeing along that axis (e.g., axis 10.4 of FIG. 1A).

Single Mode: References made to light propagation in a single transversemode are intended to include propagation in essentially or effectively asingle mode; that is, in a practical sense perfect suppression of allother modes may not always be possible. However, single mode does implythat the intensity of such other modes is either small or insignificantfor the intended application.

Suppressed HOM: The degree to which an HOM needs to be suppresseddepends on the particular application. Total or complete suppression isnot demanded by many applications, which implies that the continuedpresence of a relatively low intensity HOM may be tolerable. In manyinstances it may be sufficient to provide a high degree of attenuationof HOMs compared to attenuation in the fundamental mode. We call thissuppression relative or selective. In any event, suppressing HOMsimproves system performance by, for example, improving beam quality,reducing total insertion loss, lowering noise in the signal mode, andlowering microbend loss.

Undoped: The term undoped or unintentionally doped means that a regionof a fiber, or a starting tube used to form such a region, contains adopant not intentionally added to or controlled in the region duringfabrication, but the term does not exclude low levels of backgrounddoping that may be inherently incorporated during the fabricationprocess.

DETAILED DESCRIPTION OF THE INVENTION Bend-Compensated LMA FibersGeneral Design

In this section we describe the design of bend-compensated LMA fibersthat are configured to be coiled or bent. Thus, at least a longitudinalsegment of the LMA fiber is characterized by a bend radius R_(b). Thecoiling or bending of such LMA fibers is often an expedient to savespace or satisfy some other physical requirement of a particularapplication. Typical applications (e.g., optical fiber amplifiers andlasers) will be described in a later section.

Turning now to FIG. 1A, we show a transverse cross-section of abend-compensated, LMA optical fiber 10 in accordance with one aspect ofour invention. Fiber 10 could be single moded or multiple-moded andcomprises a core region 10.1, an annular inner cladding region 10.2surrounding the core region, and an annular outer cladding region 10.3surrounding the inner cladding region. In general, these regions areconfigured to support the propagation of signal light effectively in asingle mode (i.e., the fundamental transverse mode in the direction ofthe longitudinal axis 10.4 when coiled or bent.

To this end, fiber 10 is designed to suppress the propagation of HOMs,and, in particular, the index profile and radial dimensions of the innercladding region 10.2 are configured to suppress such HOMs. Morespecifically, in accordance with one aspect of our invention, fiber 10illustratively has a symmetric index profile of the type shown in FIG.1B; that is, the core region 10.1 has an index n_(core), the outercladding region 10.3 has an index n_(out) (illustrativelyn_(out)<n_(core)), and at least a transverse portion 10.22 of the innercladding region 10.2 has its index graded between a first value n₁proximate the outer cladding region 10.3 to a second value n₂ proximatethe core region 10.1, where n₂>n₁. Optionally, the index of theremaining portion 10.21 of the inner cladding region may not be graded.In some embodiments, however, the entire inner cladding region 10.2 maybe graded.

By symmetric index profile we mean the index profile has azimuthalsymmetry; that is, the refractive index of fiber 10 at radius r isapproximately equal for all azimuthal angles (I). Thus, symmetry isrelative to the longitudinal axis of the fiber, which defines thecylindrical coordinates. In a particular cross-section of the indexprofile (corresponding to a particular azimuthal angle φ), asillustrated in FIGS. 3A, 4A and 5A, azimuthal symmetry impliesreflection symmetry: the index at radial position r approximately equalsthe index at radial position −r. The approximate azimuthal symmetry ofthe index profile ensures that variations in orientation do not produceexcessive degradation of fiber performance (e.g. HOM suppression). Asymmetrical profile may be approximated by various fabricationtechniques including stacking, and so an ideally circular or annularregion of a symmetrical profile may be approximated by a polygon orpolygonal annulus. Accordingly, one may consider certain rotationsymmetries (e.g. 4-fold or higher rotation symmetry) as providing anapproximate azimuthal symmetry.

In order to suppress HOMs we impose two criteria on this embodiment ofthe LMA fiber design. One criterion relates to the slope of the gradedindex portion of the inner cladding region 10.2; the other relates tothe radial dimensions of the inner cladding region. Thus, we prefer thatthe slope of the graded index portion of the inner cladding region 10.22is approximately equal to γn_(core)/R_(b), where γ is equal 0.6-1.2;that is, γ=1 would ideally compensate the bend according to well-knowngeometrical conformal mapping [see, Marcuse, Appl. Opt., Vol. 21, p.4208 (1982)], but preferred designs may include a stress correction(e.g., γ=0.8) or other adjustments that allow for curvature variationswithin a coil, etc. In addition, in some embodiments we prefer that theratio of the outer radius r₂ to the inner radius r₁ of the innercladding region 10.2 satisfies the inequality r₂/r_(core) 2 and inothers we prefer that r₂/r_(core)>3 depending on the desired level ofHOM suppression. More specifically, our simulations demonstrate that amoderately thick inner cladding region (r₂/r_(core)>2) gives about 1 dBof HOM loss for every 0.1 dB of fundamental mode loss (i.e., HOM loss isabout 10× fundamental mode loss), whereas a thicker inner claddingregion (r₂/r_(core)>3) provides much higher selectivity—about 10 dB ofHOM loss for every 0.1 dB of fundamental mode loss (i.e., HOM loss isabout 100× fundamental mode loss).

The impact of the inner cladding region on bend compensation andrelative HOM suppression can be better appreciated by considering theindex profiles shown in FIGS. 2A & 2B and FIGS. 3A & 3B. For purposes ofillustration only the profiles of step-index-core (SIC) fibers aredepicted in all four figures, but FIG. 2 illustrates a conventional SICfiber subject to a loose bend (FIG. 2A) and a tighter bend (FIG. 2B),whereas FIG. 3 illustrates a SIC fiber with a portion of the innercladding graded in accordance with one embodiment of our invention. Thecase where the fiber is subject to no bend (FIG. 3A) is compared to thecase where the fiber is subject to a relatively tight bend (FIG. 3B).

Thus, FIG. 2A includes two equivalent index profiles for the case wherea conventional SIC fiber is subject to no bend (profile 20) and to arelatively loose bend (profile 22; e.g., R_(b) 50 cm). The innercladding 20.2 of the conventional SIC fiber has a uniform or constantindex; that is, the inner cladding has no graded index portion. In FIG.2A, the two equivalent index profiles approximate one another. Thefundamental mode (effective index 24) is fully guided, but the HOMs(designated by a single effective index 26 for simplicity) experiencetunneling loss, as indicated by wavy arrow 28. Therefore, the tunnelingloss of the HOMs is much greater (infinitely greater in theory) thanthat of the fundamental mode.

As the bend becomes tighter (smaller bend radius; e.g., R_(b)˜15 cm),the slope of the index profile increases, as illustrated by profile 23(FIG. 2B). Under these circumstances, both the fundamental mode and theHOMs experience macrobend tunneling loss as indicated by wavy arrows 29and 28, respectively. [Macrobend loss is the tunneling of a mode fromthe core region into a portion of the cladding region where theequivalent index (as indicated by the profile 23) is larger than themode effective index (as indicated by level 24 in the core region20.1).] Because the fundamental mode is no longer fully confined to thecore region, the ratio of HOM-to-fundamental loss for FIG. 2B is smallerthan for FIG. 2A.

One of the key principles we have come to recognize is that the relativeconfinement of the fundamental mode and the HOMs is determined primarilyby the properties of the inner cladding region, particularly the portionof the inner cladding region 30.2 on the outside of the bend. FIGS. 3A &3B schematically demonstrate how inner cladding region impacts bendcompensation and relative fundamental-mode-to-HOM confinement (orsuppression). Thus, FIG. 3A depicts equivalent index profiles for twostraight (no bend) fibers—profile 20 is the index profile of aconventional SIC fiber (as in FIG. 2A) and profile 30 is the indexprofile of a symmetric-bend-compensated (SBC) fiber in which a portion(30.2 g) of the inner cladding region 30.2 proximate the outer claddingregion 30.3 is graded in accordance with an illustrative embodiment ofour invention. (In contrast, the remaining portion 30.2 ng proximate thecore region 30.1 is not graded.) When the SBC fiber is subjected to arelative tight bend (e.g., R_(b)˜15 cm), the profiles change (tilt) asshown in FIG. 3B; that is, the profile 20 of the conventional SIC fiberof FIG. 3A tilts becoming the shape indicated by profile 23 of FIG. 3B.Likewise, the profile 30 of our inventive SBC fiber also tilts becomingthe shape indicated by profile 33 of FIG. 3B, but the graded innercladding region has a significant effect in reducing macrobend loss ofthe fundamental mode. More specifically, the fundamental mode (wavyarrow 29) must tunnel through a much longer radial distance in ourinventive fiber than in a conventional SIC fiber. This relationship isrepresented by the inequality r_(c2)>>r_(c1), where r_(c2) is theintersection of an extension of the effective index line 24 of thefundamental mode with the index profile 33 of our inventive SBC fiber,and r_(c1) is the intersection of the same extension of the effectiveindex line 24 of the fundamental mode with the index profile 23 of theconventional SIC fiber. In contrast, tunneling of the HOMs is relativelyunaffected, so that the relative confinement of the fundamental mode isgreatly improved.

The schematic illustration of FIG. 3 thus shows how our invention canimprove fundamental-mode confinement. Since bend loss, effective modearea (A_(eff)) and HOM suppression have well known tradeoffs, oneskilled in the art can readily apply the principles above to achieveimprovements in any of the three.

In addition, we have assumed a step-index (i.e., a constant index in theradial dimension) for the core region of our inventive fibers above onlyas a pedagogical convenience. Our bend compensation strategy iscompatible with a variety of core region index profiles, including, forexample, graded profiles such as linearly graded profiles orparabolically graded profiles, or profiles in which the grading isapproximately linear or approximately parabolic. Alternatively, the coreregion profile may include peaks (at/near the center, at/near the outeredge, or both) superimposed on a graded profile. However, the well knownadvantages of a parabolic core index profile (insensitivity of modeshape to bend radius; low mode displacement) are particularly usefulwhen combined with a bend-compensated inner cladding design of the typedescribed above.

Many embodiments of our invention utilize an overall symmetric indexprofile, which simplifies both fiber fabrication and apparatus assembly[e.g., at least one optical property such as fundamental mode size,signal attenuation, dispersion, etc. is rendered essentially independentof the azimuthal orientation of the fiber with respect to the directionof the bend]. However, it may nevertheless be advantageous toincorporate the above-described inner cladding features to control HOMsuppression in a LMA fiber having an overall asymmetric index profile.By overall index profile we mean the index profile across essentiallythe entire transverse cross-section of the fiber. By asymmetric indexprofile we mean that in sampling the index profile vs. radius at someazimuthal angle, φ, the index profile of the LMA fiber at r is not themirror image of the index profile at −r. Thus, asymmetry is relative tothe longitudinal axis of the fiber, as illustrated in FIG. 7A. This isparticularly true when the index profile is sampled along an azimuthalangle corresponding to the direction of the anticipated bend.

Symmetric Bend-Compensated (SBC) LMA Fibers Examples

This section describes two designs (designated A and B) ofbend-compensated SBC LMA fibers in accordance with illustrativeembodiments of our invention. In both of these fiber design the coreregion is parabolically graded and at least a portion of the innercladding regions has linearly graded index, but they differ in thepresence (Example A) or absence (Example B) of a step in the indexprofile at the interface between the inner and outer cladding regions.According to the principles illustrated in FIG. 3B, HOMs must be allowedto leak out of the inner cladding region. Therefore, the outer claddingregion index cannot be so low that it prevents HOM suppression, but itdoes not imply a specific value for the outer cladding region index.Thus, designs with and without the aforementioned index step may bedesirable.

As SBC fibers, both designs also have approximately symmetric indexprofiles.

FIG. 4A shows the index profile 40 a of Example A2, an LMA fiber(unbent) having the following features: a circular core region 40.1 witha parabolic index profile 40.1 a; an annular inner cladding region 40.2with a linearly graded index profile 40.2 a (e.g., graded from Δn₂˜0 atr₁ to Δn₁˜6×10⁻⁴ at r₂), an annular outer cladding region 40.3 having auniform (or constant) index profile 40.3 a, and an index step 40.5 a atthe interface between the inner cladding region and the outer claddingregion. We describe below the physical characteristics and performanceof three fibers (A1, A2, A3) of the same design type as fiber A2.

Similarly, FIG. 5A shows the index profile 50 of Example B, asingle-mode, LMA fiber (unbent) having the following features: acircular core region 50.1 with a parabolic index profile 50.1 a; anannular inner cladding region 50.2 with a linearly graded index profile50.2 a (e.g., graded from Δn₂˜4×10⁻⁴ at r₁ to Δn₁˜0 at r₂), and anannular outer cladding region 50.3 having a uniform (or constant) indexprofile 50.3 a. In contrast with Example A, the LMA fiber of Example Bhas no index step at the interface between the inner cladding region andthe outer cladding region. We describe below a single fiber having thephysical characteristics and performance of this design.

Table I lists various physical characteristics of the LMA fibers ofExamples A and B, as indicated by FIG. 4A and FIG. 5A, respectively, aswell as a performance characteristic (e.g., A_(eff)) as indicated byFIG. 6. For all of these example fibers, D_(core)=2r₁.

TABLE I n_(out) − n₁ A_(eff) n_(core) − n_(out) n₂ − n₁ r₁ r₂ (n₂ −n₁)/(r₂ − r₁) “step” Example (μm²) (×10⁻⁴) (×10⁻⁴) (μm) (μm) r₂/r_(core)(m⁻¹) (×10⁻⁴) A1 1100 2.7 7.7 20 120 6 7.7 7.7 A2 ~1620 3.1 6.2 40 120 37.8 6.2 A3 ~2020 2.9 9.3 40 160 4 7.8 9.3 B 1050 7.3 3.8 30 80 ~2.7 7.60

For each of these fibers, (n₂−n₁)/(r₂−r₁)≈7.7/m, in agreement with therequirement that this slope compensate the bend induced gradientγn_(core)/R_(b)=7.7/m. In this gradient calculation, we assumed γ=0.8(to accommodate stress in the fiber), R_(b)=15 cm (a representative bendradius requirement for reasonable coil size of a LMA fibers in anoptical fiber amplifier), and n_(core)=1.45. The index value of 1.45corresponds to that of pure (undoped) silica at a wavelength of about1000 nm and is a good approximation to the index (i) at otherwavelengths of interest (e.g., n_(core)=1.444 at a wavelength of about1550 nm) and (ii) at other doping levels typical of doped core regionsof LMA fibers (i.e., index differences due to doping are typically muchless than 0.01; these differences are important for guidance, but havenegligible impact on this expression for the bend-induced gradient).

When the above LMA fibers are coiled or bent to a radius R_(b)=15 cm,our simulations show that the bend-compensated index profiles 40 a and50 a of FIGS. 4A and 5A, respectively, change (tilt and reconfigure) tothe equivalent index profiles 40 b and 50 b of FIGS. 4B and 5B,respectively. More specifically, in the coiled or bent fiber the indexprofile 40 b of FIG. 4B has shifted up on the right side (positiveradial distances toward the outside radius of the bend, which increasesindex) and down on the left (negative radial distances toward the insideradius of the bend, which decreases index). Consequently, the gradedportion 40.2 a of the inner cladding region 40.2 (FIG. 4A) reconfiguresinto the horizontal portion 40.2 b (FIG. 4B). Likewise, the paraboliccore region index profile 40.1 a reconfigures into an equivalent index“hump” 40.1 b, which guides the fundamental mode in the bent or coiledsegment of the overall LMA fiber. Thus, FIG. 4B indicates that actualguidance in coiled or bent fiber with R_(b)=15 cm is provided by anequivalent index peak Δn˜1×10⁻⁴, which would be the approximateprecision required in fabrication of the fiber.

Our simulations show that both of the designs described above haveexcellent performance characteristics, as illustrated by FIG. 6, whichshows HOM suppression vs. effective mode area (A_(eff)) for a bothconventional LMA designs (curve 6.6 for a conventional SIC fiber; curve6.5 for a conventional fiber having a parabolic index core region) andour inventive LMA designs (curves 6.1-6.4). The key design tradeoffs areamong fundamental mode area, HOM suppression, and bend loss. This threeway tradeoff can be illustrated in a two-dimensional plot by comparingdesigns with the same fundamental bend loss. FIG. 6 shows such acomparison, where the fundamental bend loss is approximately 0.1 dB/mfor all designs. This particular bend loss value was selected so thatthe total loss in a few-meter-long segment of gain fiber would betolerable (e.g., 0.5 dB in 5 m). This procedure can be applied withdifferent values of fundamental loss, bend radius, etc. according tovarious system-level design requirements (e.g., length required foradequate pump absorption, acceptable package size, etc).

The SBC designs (curves 6.1-6.4) span a range of desirable HOM vs.A_(eff) performance results: some have very large mode areas (˜2000 μm²;r₂=160 μm; r₂/r_(core)=4; design A3, curve 6.3) with robust single-modebehavior (e.g., a LMA fiber length of 5 m with fundamental loss of only0.5 dB but HOM loss greater than 100 dB; i.e., the HOM loss is 200× thefundamental mode loss). Others (designs A1, A2 on curve 6.1; design B oncurve 6.4) have even more robust single-mode operation (i.e., higher HOMloss) but at the expense of smaller mode areas (e.g., 500-1700 μm²).

Among the preferred examples, designs with a relatively thin innercladding region (r₂/r_(core)=2.7; design B of curve 6.4) still have avery impressive combination of relatively large HOM loss (˜100 dB/m) andlarge A_(eff) (>1000 μm²). However, designs with even smallerr₂/r_(core) show significant degradation of HOM suppression (e.g.,r₂/r_(core)=2.0, HOM loss<10 for the right-most point on curve 6.4).

The calculated mode areas include the effect of bend distortion, whichmeans, for example, A_(eff)˜1200 μm² in FIG. 6 is actually much largerthan A_(eff) quoted for the prior art straight LMA fibers having a 40 μmMFD (mode-field area of ˜1256 μm²) since such fibers undergo significantbend-induced distortion and modefield reduction upon bending.

Design B (FIGS. 5A and 5B) has A_(eff)˜1000 μm² and huge HOM lossexceeding 100 dB/m. This design, which omits the index step at theinterface between the inner and outer cladding regions, may be lesssensitive to fiber fabrication variations—the index peak of the “bump”(FIG. 5B) is somewhat higher than that of Design A2 (FIG. 4B), althoughΔn is still approximately 1−2×10⁴. However, our sensitivity studiesindicate that either Design A or Design B and a fabrication irregularityin the fiber index of ˜10⁻⁴, can achieve larger mode areas thanconventional 50 μm core LMA fibers (e.g., leakage channel fibers;step-index core fibers) with robust single-mode operation, enabled by˜50 dB of total HOM suppression over 5 m (a typical length of the GPF inan optical fiber amplifier).

Asymmetric Bend-Compensated (ABC) LMA Fibers

To achieve asymmetry in the overall index profile of an LMA fiber it isimportant to be able to control the refractive index of the glass inminute regions of the fiber cross-section. One way to achieve suchcontrol is to fabricate the fiber as a microstructure; that is, amultiplicity of glass cells or voids in which the index of each cell isindividually controllable during fabrication and the overall index of aregion (e.g., a cell, core, or cladding) is the average of the indicesof the cells (and surrounding matrix, if present) within that region.

Thus, microstructure cells may be fabricated, using techniques wellknown in the art, from commercially available glass (silica) rods thathave slightly different refractive indices; e.g., F300 rods are dopedwith chlorine so that the index of the rod is about 3.5×5×10⁻⁴ abovethat of pure silica, and F320 rods are doped with fluorine so that theindex of the rod is approximately 6−14×10⁻⁴ below that of pure silica.Although the diameter of each rod is not critical, it is conveniently inthe range of approximately 1-2 mm. Obviously, by arranging F300 and F320rods in various combinations it is possible to make minute adjustmentsin the index of cells, and hence the index of various fiber regions. Onetechnique for achieving an index between that of F300 and F320 rods isto overclad one type of glass rod (e.g., F320) with the other type(e.g., F300). By controlling the volume (or cross-sectional area) ofeach glass rod in the overclad assembly any index between the two can beobtained.

F300 and F320 rods are commercially available from Heraeus QuarzglasGmbH, Hanau, Germany.

FIGS. 7A and 7C illustrate the index profile of an unbent,microstructured, asymmetric bend-compensated (ABC) fiber in accordancewith a second aspect of our invention. A cross-section of the profile isshown in FIG. 7A, while the two-dimensional structure of the profile isillustrated in FIG. 7C. The index profile is comprised of constant-indexhexagonal cells arranged in a triangular lattice, with center-to-centerspacing L=10 μm between cells. The innermost 19 cells comprise the coreregion 70.1, so that the core radius r₁=2.5 L=25 μm. The claddingextends to r₂=9 L=90 The step-wise nature of the profile in FIG. 7Areflects the minute control of the local index within the fibercross-section. Each step is 10 μm wide, and the index of one stepdiffers from that of any adjacent step by approximately 0.8×10⁻⁴. Thecollection of individual index steps are configured to realize an unbentfiber, asymmetric index profile 70 a including an approximately circulargraded-index core region 70.1, an annular graded-index inner claddingregion 70.2, and an annular outer cladding region 70.3.

The core region 70.1 has a radius r₁ (e.g., r₁=25 μm), and the innercladding region 70.2 has a thickness r₂−r₁ (e.g., r₂−r₁=65 μm). Aspreviously discussed in the description of SBC fibers, here again forHOM suppression the ratio r₂/r_(core)>2 in some embodiments of our ABCfibers, and r₂/r_(core)>3 in others. In the example shown in FIG. 7A,r₂/r_(core)=9 L/2.5 L=3.6. In addition, the steps between adjacent cells(within the core region and within the inner cladding region)approximate a slope of the index profile needed to pre-compensate thebend-induced gradient γn_(core)/R_(b). That is, the steps approximate agradient of the index step over the step spacing=0.8×10⁻⁴/10 μm=8/meter.The bend induced gradient is γn_(core)/R_(b)=0.8(1.45)/15 cm=7.7/meter.Here, we have used the representative value 1.45 for n_(core); the coreindex is not constant, but the variations in index have a negligibleimpact on the gradient formula.

In this ABC fiber embodiment, FIG. 7A also illustrates several featuresthat differentiate ABC and SBC designs. First, in ABC designs the gradedcore index in some portions (on the “left” side of the fiber axis, thatis, the portion intended for the inside of the expected bend) extendsabove that of other portions (on the “right” side of the fiber axis,that is, the portion intended for the outside of the expected bend).Likewise, the graded inner cladding index has two portions: on the leftside, the inner cladding index extends above that of the core region,whereas on the right side, it extends below that of the core region.However, when the ABC fiber of FIG. 7A is bent or coiled to a bendradius R_(b)=15 cm, the overall profile changes (tilts and reconfigures)itself, as shown in equivalent index profile of FIG. 7B; that is, theprofile 70 b flattens across the core and inner cladding regionsresulting in, on average, essentially a step-index core profile 70 c.The core-to-inner cladding contrast is typically small; in thisillustration the contrast is only about 1×10⁻⁴.

In general, in our ABC designs r₂ is measured from the center of thecore region to the outermost edge of the annular inner cladding in thedirection pointing toward the outside of the bend. Some embodiments ofour invention take advantage of an off-center core region to make r₂larger (even though the less relevant distance r1 is made smaller.

An ABC fiber should include a means for fixing the orientation of thefiber cross-section relative to the bend. This fixing means shouldeither mechanically fix the orientation or assist in measuring theorientation, so that orientation alignment can be performed. Such meansare known in the art, including placing a marker along its length toidentify the azimuthal orientation of the fiber; i.e., the direction inwhich the fiber should be bent. For example, the fiber cross-section mayhave a high aspect ratio (e.g., a “ribbon” fiber) to mechanicallyprevent orientation drift. A marker may include a flat or groove (notshown) located on the outer cladding surface on the outside radius ofthe bend.

Asymmetric Bend-Compensated (ABC) LMA Fibers Examples

Several ABC fiber designs of the type described above have beensimulated with cell spacing L, core diameter D_(core)=2r₁=5 L (19 cellswithin the core region) and with inner cladding sizesD_(i-clad)=(r₂−r₁)=12 L [D_(i-clad)/D_(core)=r₂r/r_(core)=2.4] or 18 L[D_(i-clad)/D_(core)=r₂/r_(core)=3.6]. In an illustrative design withL=10, the bend-compensating gradient (slope of the inner cladding region70.2) corresponded to steps along the x-axis of approximatelyγ×n_(sil)/R_(b), or approximately 0.8×10⁻⁴, as shown in FIG. 7A, wheren_(sil) is the index of pure silica (a good approximation to n_(core) asindicated earlier) and R_(b) is assumed to be 15 cm, a fairly large butpractical coil size.

A relatively small core-to-inner cladding contrast was used (for theapproximate step-index core profile 70 c, FIG. 7B) to enhance leakage ofHOMs while provide acceptable calculated bend loss for the fundamentalmode of 0.1 dB/m. Our simulations confirmed that very large mode area(A_(eff)=2160 μm²) is compatible with large suppression of HOMs (HOMloss ˜140 times the fundamental mode loss).

The advantages of our ABC strategy can be better understood by comparingthe performance tradeoffs of our ABC fibers with several prior artdesigns, as indicated by FIG. 8. The three-way tradeoff between bendloss, HOM suppression, and effective mode area is summarized there bylocking all fiber designs to a calculated bend loss of 0.1 dB/m atR_(b)=15 cm and plotting relative HOM suppression (i.e., HOMloss/fundamental mode loss) vs. A_(eff). The prior art step-index corefiber (curve 8.6) and the prior art parabolic-index core fiber (curve8.5) reduce to simple curves since they have only two degrees of freedom(contrast is locked/fixed for each core region size by the 0.1 dB/m bendloss requirement). These curves confirm that prior art step-index coredesigns cannot be scaled significantly above 1000 μm² for typicalcoiling requirements because of a tradeoff with HOM suppression. Priorart parabolic-core index fibers show a significantly improved tradeoff,but they are still limited in area when significant bend-losssuppression of HOMs is required.

The mode areas of FIG. 8 were calculated at the assumed bend radius of15 cm, which is a realistic size for a LMA fiber during amplifieroperation. This type of calculation is more relevant than straight-fiberareas often quoted in the prior art, which can differ in area by afactor of two or more relative to the bent configuration.

In contrast, our simulated ABC fibers (three data points 8.2, three datapoints 8.3) illustrate a qualitatively different type of behavior,confirming that our strategy essentially removes the tradeoff with area.The core region size of ABC fibers is increased by scaling L, whereasthe contrast is adjusted to meet the loss requirement. The results showthat mode area is increased with little impact on the HOM suppressionratio. The HOM suppression is essentially determined by the relativesize of the cladding region alone; that is, by the ratioD_(i-clad)/D_(core)=r₂/r_(core) alone.

Our ABC fibers can thus remove a fundamental limitation on mode areathat constrains prior art strategies. Our fibers can achieve mode areasin the 2000-3000 μm² range with a level of single modedness—and thusbeam quality—analogous to conventional, prior art fibers with muchsmaller A_(eff)˜600-700 μm². In the A_(eff)˜1000 μm² regime, priorstep-index and parabolic-index core designs are not only very difficultto make with conventional fabrication methods, they also fail to providerobust HOM suppression even when fabrication is “perfect.” For example,a 5 m long step-index core prior art fiber with A_(eff)˜1000 μm² and<0.5 dB total bend loss can achieve at most a meager 2-3 dB of HOMbend-loss suppression. A prior art parabolic-index core fiber canapproach a respectable 10-15 dB of HOM suppression, although actualperformance is expected to be worse than ideal calculations. In anycase, the performance of these prior art fibers falls well short oftotal HOM suppression and confirm the actual experiences of actualusers: good beam quality is achievable in prior art “hero” experimentsbut relies heavily on very careful management of input launch, fiberlayout and fiber handling.

Finally, we note that, in an optical fiber amplifier, a highly displacedfundamental mode would suffer serious gain-interaction impairment sincemost of the gain-doped region of the core area would not see the signallight. Calculations demonstrated that our ABC fibers did not exhibitsuch impairment. Thus, with >100 times relative suppression of HOMs (and0.5 dB total bend loss), our fibers exhibited a high degree of HOMsuppression (>50 dB; essentially complete) for mode areas exceeding 2000μm² or even exceeding 3000 μm². Mode intensity profiles demonstrated anexcellent fundamental mode shape and no displacement, and so thegain-doped region of the core can be tailored for high gain overlap andhigh gain selectivity.

The ultimate limit of area scaling will be determined by the precisionof index control in each cell.

Applications

A principal application of our invention is depicted in FIG. 9, a highpower (e.g., >300 W optical output) optical fiber amplifier 230comprising a LMA gain-producing optical fiber (GPF) 235 a opticallycoupled to an optional LMA pigtail fiber 235 p. GPF 235 a is opticallycoupled to a combiner 233, and pigtail fiber 235 p is optically coupledto a utilization device 234. Either GPF 235 a or pigtail 235 p, or both,is designed in accordance with our invention; that is, since either orboth of these LMA fibers would typically be coiled inside the amplifierpackage, either or both would be designed to have a bend-compensatedinner cladding region as previously described.

In a typical commercially available amplifier package, coiled LMA fibers100 (FIG. 10) or 110 (FIG. 11) are mounted on a plate 104 or a mandrel112, respectively. LMA fiber 110 (FIG. 11) is wound helically on mandrel112, whereas LMA fiber 100 (FIG. 1) is wound within a flat, circulargroove 102 in a major surface of plate 104. In each case, the plate 104or the mandrel 112 serves as a support member, serves to define (andhence predetermine) the bend radius R_(b) and fiber orientation (ifnecessary), and provides heat sinking. To this end, the plate or mandrelis made of material having a relatively high thermal conductivity (e.g.,copper). Furthermore, in each case the LMA fiber may be affixed to thesupport member by any of several means; e.g., by sticky material such asdouble-sided adhesive tape within groove 102 or on the cylindricalsurface of mandrel 112, or by potting material such as silicone appliedafter the fiber is wound on the plate or mandrel.

For use as a pigtail delivery fiber, pigtail 235 p can be held in ahelix inside a cable, with diameter and pitch configured to produce thedesired local bend radius.

In relatively low power telecommunication applications, combiner 233 isknown as a wavelength division multiplexer (i.e., a WDM); in high powerapplications it is known as a pump-combiner (e.g., a tapered fiberbundle, or bulk optic components). For simplicity, hereinafter we willdescribe this aspect of our invention in the context of high powerapplications. In this case, the pump-combiner 233 couples the outputs ofan optical input signal source 231 and an optical pump source 236 intothe GPF 235 a. The input signal source 231 generates a first-wavelengthoptical input signal, which is coupled to an input of combiner 233 via aconventional fiber 232 or via bulk optics (not shown), whereas the pumpsource 236 generates a second-wavelength optical pump signal, which iscoupled by a conventional, typically multimode, fiber 237 to anotherinput of combiner 233.

As is well known in the art, the pump signal generates a populationinversion in the GPF 235 a, which amplifies the input signal from inputsource 231. The amplified input signal propagates along GPF 23 a (andthrough pigtail 235 p, if present) to utilization device 234. In highpower applications the latter may include myriad well known devices orapparatuses; e.g., another optical amplifier, a beam collimator, a lenssystem, a work piece (e.g., for cutting or welding).

Illustratively, the input source 231 is a laser that generates arelatively low power optical input signal at a wavelength in theamplification range of the GPF 235 a, whereas the pump source 236 ispreferably a semiconductor laser, but optionally could be an array ofsemiconductor light emitting diodes (LEDs). In either case, pump source236 generates a relatively high optical power (e.g., above about 150 mW)pump signal at a shorter wavelength that produces the desiredamplification of the input signal. Illustratively, the GPF 235 a israre-earth-doped fiber (e.g., preferably a ytterbium-doped fiber) oroptionally a chromium-doped fiber. In the preferred ytterbium fibercase, the signal source 231 generates an input signal having awavelength of about 1080 nm, and the pump source 236 generates a pumpsignal at a wavelength of about 915 nm, or alternatively at about 975nm.

Although the amplifier 230 of FIG. 12 depicts a common co-propagatingpump configuration (i.e., the pump and input signals propagate in thesame direction through the GPF), it is also possible to use acounter-propagating configuration (i.e., the pump and input signalspropagate in opposite directions through the GPF). In addition, amultiplicity of amplifiers may be arranged in tandem, a scheme that iswell known in the art for increasing the total gain of a high powermulti-stage system. Pump energy may also be transversely coupled intothe amplifier.

It is to be understood that the above-described arrangements are merelyillustrative of the many possible specific embodiments that can bedevised to represent application of the principles of the invention.Numerous and varied other arrangements can be devised in accordance withthese principles by those skilled in the art without departing from thespirit and scope of the invention.

In particular, the optical amplifier described above may be modified tofunction as a laser by providing a well-known optical resonator [e.g.,by using fiber Bragg gratings or bulk optic elements (e.g., mirrors) toprovide optical feedback]. Such a laser could be used as a femtosecondoscillator, which is known to produce high peak power optical pulses. Assuch, nonlinearity tends to be a problem, which can be ameliorated byusing bend-compensated LMA fibers in accordance with our invention.

When the amplifier apparatus is configured to operate as a laser, thensignal source 231 is omitted and the signal light described above wouldbe equivalent to the stimulated emission generated internally by thelaser.

We claim:
 1. A bend-compensated large mode area (LMA) optical fibercomprising: a core region having a longitudinal axis, a cladding regionsurround said core region, said core and cladding regions configured tosupport and guide the propagation of signal light at a predeterminedwavelength λ, in a fundamental transverse mode in said core region inthe direction of said axis, wherein the effective mode area of said LMAfiber is at least 90λ², said fiber being characterized by a transversecross-section that is further characterized by a refractive indexprofile, said cladding region including an inner cladding regionsurrounding said core region and an outer cladding region surroundingsaid inner cladding region, at least one longitudinal segment of saidfiber being configured to be bent or coiled to a bend radius R_(b),which bend radius would change a gradient of said index profile withinsaid segment, and at least said segment being precompensated in that (i)said index profile is approximately azimuthally symmetric with respectto said axis and (ii) the refractive index of at least a transverseportion of said inner cladding region is graded with a slope configuredto compensate for the expected change of said gradient associated withsaid fiber being bent or coiled.
 2. The fiber of claim 1, wherein saidinner cladding region includes said graded radial portion locatedproximate said outer cladding region and a remaining portion locatedproximate said core region.
 3. The fiber of claim 2, wherein therefractive index of said remaining portion is not graded.
 4. The fiberof claim 2, wherein the refractive index of said remaining portion isalso graded.
 5. The fiber of claim 1, wherein the effective mode area ofsaid LMA fiber is at least 300λ₂.
 6. The fiber of claim 1, wherein saidslope is approximately γn_(core)/R_(b), where n_(core) is the refractiveindex of the core region and γ=0.6-1.2.
 7. The fiber of claim 1, whereinthe fiber has optical properties and said longitudinal segment isconfigured so that at least one of said optical properties isessentially independent of the orientation of said fiber with respect tothe direction of the bend in said bent or coiled segment.
 8. The fiberof claim 1, wherein said inner cladding region is annular having aninner core radius beginning at r_(core) and an outer radius r₂ such thatthe ratio r₂/r_(core) is configured to suppress the propagation ofhigher order modes in said fiber.
 9. The fiber of claim 8, whereinr₂/r_(core)>2.
 10. The fiber of claim 9, wherein said radii areconfigured so that the optical loss experienced by said higher ordermodes is at least 10× the optical loss of said fundamental mode.
 11. Thefiber of claim 8, wherein r₂/r_(core)>3.
 12. The fiber of claim 11,wherein said radii are configured so that the optical loss experiencedby said higher order modes is at least 100× the optical loss of saidfundamental mode.
 13. The fiber of claim 8, wherein said transverseportion of said inner cladding region has a higher index proximate saidcore region and a lower index proximate said outer cladding region. 14.The fiber of claim 13, where said lower index is less than that of saidouter cladding region.
 15. The fiber of claim 13, wherein said lowerindex is approximately equal to that of said outer cladding region. 16.The fiber of claim 1, wherein said core region has a parabolic indexprofile.
 17. A bend-compensated LMA optical fiber comprising: a coreregion having a longitudinal axis and a radius, r_(core), a claddingregion surround said core region, said core and cladding regionsconfigured to support and guide the propagation of signal light at apredetermined wavelength λ in a fundamental transverse mode in said coreregion in the direction of said axis, wherein the effective mode area ofsaid LMA fiber is at least 90λ² said fiber being characterized by atransverse cross-section that is further characterized by a refractiveindex profile, said cladding region including an inner cladding regionsurrounding said core region and an outer cladding region surroundingsaid inner cladding region, wherein said inner cladding region comprisesat least a transverse portion of said inner cladding region graded witha slope, at least a longitudinal segment of said fiber that when bent orcoiled to a bend radius R_(b), said bend or coiling would introduce achange to said index profile within said segment, and within saidsegment the refractive index of at least a portion of said innercladding region is graded with a slope configured to compensate for theexpected change of said gradient, and said inner cladding region beingannular having an outer radius r₂ such that the ratio r₂/r_(core) isconfigured to suppress the propagation of higher order modes in saidfiber.
 18. The fiber of claim 17, wherein said inner cladding regionincludes said transverse portion located proximate said outer claddingregion and a remaining portion located proximate said core region. 19.The fiber of claim 18, wherein the refractive index of said remainingportion is not graded.
 20. The fiber of claim 18, wherein the refractiveindex of said remaining portion is also graded.
 21. The fiber of claim17, wherein the effective mode area of said LMA fiber is at least 300λ².22. The fiber of claim 17, wherein said transverse cross section has anoverall refractive index profile that is symmetric with respect to saidfiber axis.
 23. The fiber of claim 17, wherein said transverse crosssection has an overall refractive index profile that is asymmetric withrespect to said fiber axis.
 24. The fiber of claim 17, wherein saidslope is approximately γn_(core)/R_(b), where n_(core) is the refractiveindex of the core region and γ=0.8-1.0.
 25. The fiber of claim 17,wherein r₂/r_(core)>2.
 26. The fiber of claim 25, wherein said radii areconfigured so that the optical loss experienced by said higher ordermodes is at least 10× the optical loss of said fundamental mode.
 27. Thefiber of claim 17, wherein r₂/r_(core)>3.
 28. The fiber of claim 27,wherein said radii are configured so that the optical loss experiencedby said higher order mode is at least 100× the optical loss of saidfundamental mode.
 29. A bend-compensated LMA optical fiber comprising: acore region have a longitudinal axis and a parabolic index profile, saidcore region having a core radius, r_(core), a cladding regionsurrounding said core region, said core and cladding regions configuredto support and guide the propagation of signal light in a fundamentaltransverse mode in said core region in the direction of said axis, saidfiber being characterized by a transverse cross-section that is furthercharacterized by a refractive index profile, said cladding regionincluding an inner cladding region surrounding said core region and anouter cladding region surrounding said inner cladding region, whereinsaid inner cladding region comprises at least a transverse portion ofsaid inner cladding region graded with a slope, at least a longitudinalsegment of said fiber that when bent or coiled to a bend radius R_(b),said bend or coiling would introduce a change to said index profilewithin said segment, and within said segment, said slope isapproximately equal to γn_(core)/R_(b), where n_(core) is the refractiveindex of said core region and γ=0.6-1.2, and said inner cladding regionbeing annular having an outer radius r₂ such that the ratio r₂/r_(core)is configured to suppress the propagation of higher order modes in saidfiber, wherein r₂/r_(core)>2.
 30. The fiber of claim 29, wherein saidinner cladding region includes said transverse portion located proximatesaid outer cladding region and a remaining portion located proximatesaid core region.
 31. The fiber of claim 30, wherein the refractiveindex of said remaining portion is not graded.
 32. The fiber of claim30, wherein the refractive index of said remaining portion is alsograded.
 33. The fiber of claim 29, wherein the effective mode area ofsaid LMA fiber is at least 300λ², where λ is the wavelength of saidsignal light.
 34. The fiber of claim 29, wherein said transverse crosssection has an overall refractive index profile that is symmetric withrespect to said fiber axis.
 35. The fiber of claim 29, wherein saidtransverse cross section has an overall refractive index profile that isasymmetric with respect to said fiber axis.
 36. A bend-compensated LMAoptical fiber comprising: a core region having a longitudinal axis and aradius, r_(core), a cladding region surround said core region, said coreand cladding regions configured to support and guide the propagation ofsignal light at a redetermined wavelength λ in a fundamental transversemode in said core region in the direction of said axis, wherein theeffective mode area of said LMA fiber is at least 90λ², said fiber beingcharacterized by a transverse cross-section that is furthercharacterized by a refractive index profile, said cladding regionincluding an inner cladding region surrounding said core region and anouter cladding region surrounding the inner cladding region, at least alongitudinal segment of said fiber being configured to be bent or coiledto a bend radius R_(b), which bend radius would change a gradient ofsaid index profile within said segment, and at least said segment beingpre-compensated in that (i) said index profile is azimuthally symmetricwith respect to said axis and (ii) the refractive index of at least atransverse portion of said inner cladding region is graded with a slopeconfigured to increase the loss of HOMs when said fiber is bent to saidradius R_(b).